Welcome!

Hello there, and welcome to my little corner of the Internet, in which I attempt to give the interested layperson some idea of what modern mathematics is about. I appreciate any feedback you have: yuri@lmqm.xyz.

Jacob Lurie has said that “mathematics is a giant playground filled with all kinds of toys that the human mind can play with, but many of these toys have very long operating manuals”. I am fortunate that my areas of study, topology and geometry, are very visual subjects, which makes them somewhat easier to convey.

I will make little to no mention of real-world applications of the concepts I discuss here. I do not want to give the impression that applications are sparse: even the most abstract concepts discussed here turn out to have many important and unexpected applications to real-world problems in a wide variety of other disciplines. However, being a theoretician myself, I for the most part don’t know what they are, or am not familiar enough with them to do them justice. Applications are of course interesting and important, but that’s a project for someone else.

Acknowledgements

Undoubtedly, the greatest intellectual debt of this project is to George Peschke. My conversations with him have profoundly shaped my views of mathematics and of mathematical pedagogy, and transformed my imagination of what is possible in mathematics education.

The University of Alberta's Undergraduate Research Initiative provided financial support for a predecessor of this project. The interactive video ("ractive") technology employed here was developed during late nights at the Hausdorff Institute for Mathematics. The University of Texas Libraries provided a private office for recording audio.

Riley Meth provided valuable assistance and encouragement at an early stage of this project, and her work ethic remains a source of inspiration. Joel Adria and Joe Belzberg provided stylistic advice. Alex Yarosh gave bug reports and feedback.

Ractives

The term comes from The Diamond Age. The source is available on GitHub:

These are a bit messy and have no documentation yet, but will work if you really want to get your hands on this as soon as you can.